DANANG, Vietnam — President Trump said on Saturday that he believed President Vladimir V. Putin was sincere in his repeated denials of interference in the 2016 presidential elections, calling the investigations into Moscow’s meddling a politically motivated “hit job” that is hindering cooperation with Russia on life-or-death issues.

Speaking after meeting privately with Mr. Putin on the sideline of the Asia Pacific Economic Cooperation summit meeting in Danang, Vietnam, Mr. Trump said he had again asked whether Russia had meddled in the contest, but the continued focus on the issue was insulting to Mr. Putin.

He suggested it was time to move past the issue so that the United States and Russia could cooperate on confronting the nuclear threat from North Korea, solving the Syrian civil war, and working together on Ukraine.

“He said he didn’t meddle — I asked him again,” Mr. Trump told reporters traveling with him aboard Air Force One. “You can only ask so many times. I just asked him again. He said he absolutely did not meddle in our election. He did not do what they are saying he did.

“Every time he sees me he says, ‘I didn’t do that,’ and I really believe that when he tells me that, he means it. He says, ‘I didn’t do that.’ I think he is very insulted by it, which is not a good thing for our country.”

Mr. Trump did not answer a direct question about whether he believed Mr. Putin’s denials, which contradict the assessment of American intelligence agencies that the Russian president had directed an elaborate effort to interfere in the vote.

But he said that lingering questions about whether his campaign aides had worked with Russian operatives to sway the election were souring Washington’s relationship with Moscow on a host of vital security issues.

Mr. Trump also said that the continued focus on whether his campaign aides had worked with Russian operatives to sway the election was souring Washington’s relationship with Moscow and was blocking progress on vital security issues, such as confronting the nuclear threat from North Korea and ending the Syrian civil war.

“Having a good relationship with Russia is a great, great thing,” Mr. Trump said. “This artificial Democratic hit job gets in the way, and that’s a shame, because people will die.”

The allegations of collusion are the subject of an investigation by the special counsel Robert S. Mueller III, as well as multiple congressional inquiries.

Mr. Trump’s comments about the Russian president and his warning about deteriorating Moscow ties came after the close of the APEC conference here in Danang, Vietnam, where the White House steered clear of a formal meeting between the two men, but he and Mr. Putin did confer informally.

The small group of reporters who travel with Mr. Trump were barred from covering his activities for most of Saturday, leaving them in the dark about the two presidents’ interactions.

The Kremlin later released a statement saying that the leaders had met and struck an agreement on Syria. Mr. Trump then told reporters that he had had two or three brief conversations with Mr. Putin, mostly about Syria.

The United States and Russia later issued a joint statement on Syria that reaffirmed previous commitments to defeat the Islamic State and to untangle conflicts between their forces on the Syrian battlefield.

It said that Mr. Trump believed he had “ a good meeting” with Mr. Putin on joint efforts that, once in place, would “save thousands of lives.”

Mr. Trump did not answer a direct question about whether he believed Mr. Putin’s denials, which contradict the assessment of American intelligence agencies that the Russian president had directed an elaborate effort to interfere in the vote.

The folks who work in our intelligence agencies must be incredibly demoralized by these utterances by our poor excuse for a president. That he made this statement on Veterans Day adds to the pain.